Submitted by: Submitted by tamerghaly
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Words: 649
Pages: 3
Category: Other Topics
Date Submitted: 03/23/2011 06:02 PM
Real number
Rational numbers
Irrational numbers
π , √2
Integers
Whole
Natural
12
Rational Like: 34, 52,12,23
Integers {…, -3, -2, -1, 0, 1, 2, 3…….}
Whole {0, 1, 2, 3…}
Natural {1, 2, 3…}
Properties of real numbers
1- Reflexive property a = a
2- Symmetric property a = b then b = a
3- Transitive property a = b and b = c then a = c
4- Principle of substitution if a = b then we can substitute b for a in any expirations
Commutative properties
a + b = b + a , a . b = b . a
Associative properties
a + ( b + c ) = ( a + b ) + c = a + b + c
a . ( b . c ) = ( a . b ) . c = a . b . c
Distributive properties
a . ( b + c ) = a . b + a . c
( a + b ) . c = a . c + b . c
Identity Properties
0 + a = a + 0 = a
a . 1 = a . a = a
additive inverse Properties
a + (- a ) = - a +a = 0
Multiplicative inverse properties
a.1a = 1a .a=1 if b ≠ 0
Multiplication by zero
a . 0 = 0
Division properties
0a = 0 aa = 1 if a ≠ 0
Rules of signs
a(-b ) = - (ab) , (-a)b = - (ab) , ( -a ) ( -b ) = ab , - ( -a ) = a , a-b = -ab = - ab , -a-b = ab
Exponents
an = a.a.a…….a n factors , a0 = 1 if a ≠ 0 , a-n = 1an if a ≠ 0
Laws of exponents
anam= am+n , (am)n = amn , abn=anbn , aman=am-n=1an-mif a ≠0 , (ab)n= anbn , if b ≠0
Square roots
a2 =a
Geometry Review
Pythagorean Theorem
c2= a2+b2
Area = πr2
Circumference
= 2πr = πd
Area = 12bh
Geometry Formulas
Area = LW
Perimeter = 2L + 2W
Volume= πr2h
Surface area=
=πr2h+2πrh
Volume= 43πr3
Surface area=4πr2
Volume = LWH
Surface area=
2LW+ 2LH+2WH
Polynomials
Special Products
Difference of two squares
( x – a )( x + a ) = x2- a2
Squares of binomials or perfect squares
( x+a )2= x2+2ax+ a2
( x-a )2= x2-2ax+ a2
Cubes of binomials or perfect Cubes
( x+a )3= x3+3ax3+ 3a2x+a3
( x-a )3= x3-3ax3+ 3a2x+a3
Differences of two cubes
(x-a)(x2+ax+a2)=x3-a3...